The number of crystals that have formed after t hours is give by f(t) = 20e^0.013t . How long does it take for the number of crystals to triple?

Answer 1

When t=0

f(0) = 20

To triple

60 = 20 e^0.013t

e^0.013t = 3

Take the log of both sides

0.013t = ln(3)

t = ln(3)/0.013t ≈ 84.51 hours

Answer 2

Hello, Maria,

This is actually beyond my math skill, but I'll share what I found. There is no time period given, so I assumed t = 1 hour for the base case. The results in f(1hr) = 20.262 (crystals, I guess. No units are provided. Awkward.)

We want the time to produce 3X this number, or 60.785 crystals.

60.785 = 20e^0.031t

t = 85.5 hours, using Wolfram Alpha to solve.

Bob